Energies of -valued harmonic maps on polyhedra with tangent boundary conditions
A. Majumdar; J. M. Robbins; M. Zyskin
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 1, page 77-103
- ISSN: 0294-1449
Access Full Article
topHow to cite
topMajumdar, A., Robbins, J. M., and Zyskin, M.. "Energies of ${S}^{2}$-valued harmonic maps on polyhedra with tangent boundary conditions." Annales de l'I.H.P. Analyse non linéaire 25.1 (2008): 77-103. <http://eudml.org/doc/78784>.
@article{Majumdar2008,
author = {Majumdar, A., Robbins, J. M., Zyskin, M.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {harmonic maps with defects; minimal connection; bistability},
language = {eng},
number = {1},
pages = {77-103},
publisher = {Elsevier},
title = {Energies of $\{S\}^\{2\}$-valued harmonic maps on polyhedra with tangent boundary conditions},
url = {http://eudml.org/doc/78784},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Majumdar, A.
AU - Robbins, J. M.
AU - Zyskin, M.
TI - Energies of ${S}^{2}$-valued harmonic maps on polyhedra with tangent boundary conditions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 1
SP - 77
EP - 103
LA - eng
KW - harmonic maps with defects; minimal connection; bistability
UR - http://eudml.org/doc/78784
ER -
References
top- [1] Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, Dover Publications, 1965. Zbl0171.38503
- [2] Birkhoff G., Tres observaciones sobre el algebra lineal, Univ. Nac. Tacumán Rev. Ser. A5 (1946) 147-151. Zbl0060.07906MR20547
- [3] Brezis H., The interplay between analysis and topology in some nonlinear PDE problems, Bull. Amer. Math. Soc.40 (2006) 179-201. Zbl1161.35354MR1962295
- [4] Brezis H., Coron J.-M., Lieb E.H., Harmonic maps with defects, Comm. Math. Phys.107 (1986) 649-705. Zbl0608.58016MR868739
- [5] Davidson A.J., Mottram N.J., Flexoelectric switching in a bistable nematic device, Phys. Rev. E65 (2002) 051710.
- [6] de Gennes P.-G., Prost J., The Physics of Liquid Crystals, second ed., Oxford University Press, 1995.
- [7] Denniston C., Yeomans J.M., Flexoelectric surface switching of bistable nematic devices, Phys. Rev. Lett.87 (2001) 275505.
- [8] Eells J., Fuglede B., Harmonic Maps Between Riemannian Polyhedra, Cambridge Tracts in Mathematics, vol. 142, Cambridge University Press, 2001. Zbl0979.31001MR1848068
- [9] Gromov M., Schoen R., Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. IHES76 (1992) 165-246. Zbl0896.58024MR1215595
- [10] Hardt R.M., Singularities of harmonic maps, Bull. Amer. Math. Soc.34 (1997) 15-34. Zbl0871.58026MR1397098
- [11] J.C. Jones, J.R. Hughes, A. Graham, P. Brett, G.P. Bryan-Brown, E.L. Wood, Zenithal bistable devices: Towards the electronic book with a simple LCD, In: Proc IDW, 2000, pp. 301–304.
- [12] Kitson S., Geisow A., Controllable alignment of nematic liquid crystals around microscopic posts: Stabilization of multiple states, Appl. Phys. Lett.80 (2002) 3635-3637.
- [13] Kléman M., Points, Lines and Walls, John Wiley and Sons, Chichester, 1983. MR734901
- [14] Kleman M., Lavrentovich O.D., Soft Condensed Matter, Springer, 2002.
- [15] Lavrentovich O.D., Topological defects in dispersed liquid crystals, or words and worlds around liquid crystal drops, Liquid Crystals24 (1998) 117-125.
- [16] Lin F.H., Poon C.C., On nematic liquid crystal droplets, in: Elliptic and Parabolic Methods in Geometry, A.K. Peters, 1996, pp. 91-121. Zbl0876.49038MR1417951
- [17] A. Majumdar, Liquid crystals and tangent unit-vector fields in polyhedral geometries, PhD thesis, University of Bristol, 2006.
- [18] Majumdar A., Robbins J.M., Zyskin M., Elastic energy of liquid crystals in convex polyhedra, J. Phys. A37 (2004) L573-L580, J. Phys. A38 (2005) 7595. Zbl1064.58019MR2169580
- [19] Majumdar A., Robbins J.M., Zyskin M., Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra, Lett. Math. Phys.70 (2004) 169-183. Zbl1059.58009MR2109431
- [20] Majumdar A., Robbins J.M., Zyskin M., Elastic energy for reflection-symmetric topologies, J. Phys. A39 (2006) 2673-2687. Zbl1099.82019MR2213361
- [21] Majumdar A., Robbins J.M., Zyskin M., Topology and bistability in liquid crystal devices, math-ph/0611016.
- [22] Mermin N.D., The topological theory of defects in ordered media, Rev. Mod. Phys.51 (C) (1979) 591-651. Zbl0711.55009MR541885
- [23] C.J.P. Newton, T.P. Spiller, Bistable nematic liquid crystal device modelling, In: Proc. 17th IDRC (SID), 1997, p. 13.
- [24] Robbins J.M., Zyskin M., Classification of unit-vector fields in convex polyhedra with tangent boundary conditions, J. Phys. A37 (2004) 10609-10623. Zbl1138.58309MR2098054
- [25] Stewart I.W., The Static and Dynamic Continuum Theory of Liquid Crystals, Taylor and Francis, London, 2004.
- [26] Virga E.G., Variational Theories for Liquid Crystals, Chapman and Hall, 1994. Zbl0814.49002MR1369095
- [27] Volovik G.E., Lavrentovich O.D., Topological dynamics of defects – boojums in nematic drops, Sov. Phys. JETP58 (1983) 1159.
- [28] M. Zyskin, Homotopy classification of director fields on polyhedral domains with tangent and periodic boundary conditions, Preprint, 2005.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.